C-D18-DEGREE5-NECESSARY

A real proper vector at p=197 has best degree-4 bound 0 while degree 5 recovers 5/98, so degree 5 is the minimal information level

In plain language

An honest counterexample shows a fourth-order certificate can never work, and the fifth order is exactly what is needed.

Exact statement

A real proper vector at p=197 has best degree-4 bound 0 while degree 5 recovers 5/98, so degree 5 is the minimal information level